The Frenchman has been linked with a move to join up with former Saints boss Mauricio Pochettino at Tottenham, with Spurs reported to be ready to pay £20million.
Pochettino is reportedly keen for Schneiderlin and Southampton striker Jay Rodriguez to join him at White Hart Lane but executive director Les Reed and chairman Ralph Krueger are adamant that there will be no further departures from the club, prompting Schneiderlin to demand a move.
The 24-year-old France international posted a tweet on Tuesday that suggested he was unhappy to be told his future lay at St Mary's, and he has followed that up with an official transfer request despite reports he has no release clause and three years left to run on his contract.
He missed Thursday night's 3-1 friendly win at local rivals Brighton and afterwards Koeman expressed his desire not to let another one of his players head for the exit.
When asked about Schneiderlin's request to leave, Koeman told Sky Sports News: "It's the decision of the board but I don't talk about it. He's a player at Southampton and he will continue as a player at Southampton.
"But I don’t like to talk about that situation. I spoke to Morgan two days ago and he is still not in the shape to play a friendly at this level. He needs more training sessions. If he's ready he will play.
"Normally he will play next week against Bayer Leverkusen [Southampton's final pre-season friendly]."
Saints lost manager Pochettino to Tottenham at the start of the summer and several big-money sales have followed - Luke Shaw joining Manchester United, Dejan Lovren, Adam Lallana and Rickie Lambert joining Liverpool, and Calum Chambers joining Arsenal.
Reports this week are suggesting Celtic goalkeeper Fraser Forster is high on Koeman's wanted list.
Koeman added: "There is no news on that and still no news on other players. We are close to signing two or three players and we hope to do that by this weekend.
"I won't talk about any of the players but we are looking to bring in players into this squad at the level that we need to have a good season."
Regarding Thursday's reports that Manchester United striker Javier Hernandez was on Southampton's radar, Koeman said: "We like to have all the good players!"